Marco Angel Bertani-Økland

We present a graded mutation rule for quivers of cluster-tilted algebras. Furthermore, we give a technique to recover a cluster- tilting object from its graded quiver in the cluster category of cohX.

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Mutating loops and 2-cycles in 2-CY triangulated categories

Co-authored with Steffen Oppermann. To appear in Journal of Algebra

We derive a method for mutating quivers of 2-CY tilted algebras that have loops and 2-cycles, under certain specific conditions. Further, we give the classification of the 2-CY tilted algebras coming from standard algebraic 2-CY triangulated categories with a finite number of indecomposables. These algebras satisfy the setup for our method of mutation.

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Constructing tilted algebras from cluster-tilted algebras

Co-authored with Steffen Oppermann and Anette Wrålsen. Journal of Algebra 323 (2010) 2408-2428. http://dx.doi.org/10.1016/j.jalgebra.2010.02.026

Any cluster-tilted algebra is the relation extension of a tilted algebra. Given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, we present a method to construct all tilted algebras whose relation extension is the endomorphism ring of this cluster-tilting object.

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Finding a cluster-tilting object for a representation finite cluster-tilted algebra

Co-authored with Steffen Oppermann and Anette Wrålsen. Colloq. Math., 121(2): 249--263, 2010.

We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.

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